When editing showing instructions for a listing, agents have the ability to enable or disable their listing’s availability from any public broker websites (such as their brokerage’s public site, their own agent website, or any consumer-facing websites) by navigating to their listing’s Listing Worksheet via Listing Setup in ShowingTime Appointment Center.  As seen in the screenshot below, the option to "Allow real-time availability for broker websites" appears as a "Yes/No" option.

For more information about this feature, visit ShowingTime's Knowledge Base article on the topic